Lesson 25
Find Volume Using Unit Cubes
Name: Count Unit Cubes to Find Volume
Study the example problem showing how to find volume
by counting unit cubes. Then solve problems 1–8.
Example
Harry stacked blocks to make a wall. What is the volume of
the wall?
The volume of each
block is 1 cubic unit.
1 unit
1 unit
1 unit
1 cubic unit
Count the blocks in the wall to find the volume.
There are 12 blocks. The volume is 12 cubic units.
1
2
3
4
5
6
7
8
9
10 11 12
1 The green cubes show 1 layer of figure A.
Figure A has layers.
There are cubes in each layer.
The volume of figure A is cubic units.
A
2 Fill in the blanks to describe
figure B.
layers
cubes in each layer
Volume 5 cubic units
B
3 If you add another layer to figure B, what would the
volume be? Explain.
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Vocabulary
cubic unit a cube,
1 unit on each edge,
used to measure volume.
volume the amount of
space inside a solid
figure.
Lesson 25 Find Volume Using Unit Cubes
267
Solve.
4 Figure M has layers.
There are cubes in each layer.
The volume of figure M is cubic units.
5 Figure N is a rectangular prism that has twice the
M
volume of figure M. How many layers and how many
cubes in each layer could there be in figure N?
6 What is the volume of figure R? 7 How many of figure R does it take to fill figure S? How
does the volume of figure S relate to the volume of
figure R? Explain.
R
S
8 Show how to find the volume of box T. Then draw or
describe a different box that has the same volume as
box T.
T
268
Lesson 25 Find Volume Using Unit Cubes
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Lesson 25
Name: Find the Volume of a Rectangular Prism
Study the example problem showing how to use layers to find the volume
of a rectangular prism. Then solve problems 1–7.
Example
Keith uses this box to store his colored
markers. What is the volume of the box?
4 in.
2 in.
6 in.
Think about filling the box with 1-inch cubes.
One layer has 2 rows of 6 cubes, or 12 cubes.
There are 4 layers of cubes.
12 1 12 1 12 1 12 5 48 or 12 3 4 5 48
The volume of the box is 48 cubic inches.
G
1 Look at prism G.
There are layers with cubes
in each layer.
2 cm
cubes 1 cubes 5 cubes.
3 cm
The volume is cubic centimeters.
H
2 Look at prism H.
There are layers with cubes
in each layer.
layers 3 cubes 5 cubes.
The volume is cubic feet.
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2 cm
2 ft
5 ft
Lesson 25 Find Volume Using Unit Cubes
2 ft
269
Solve.
3 What is the volume of this rectangular prism?
Show your work.
2 ft
4 ft
2 ft
Solution: 4 Mia has a box that she filled with the cubes at the right.
What is the volume of Mia’s box?
Show your work.
3 in.
2 in. 1 in.
Solution: 5 A box is 2 inches long, 1 inch wide, and 6 inches tall.
What is the relationship between the volume of this
box and the one in problem 4? Tell how you know.
6 Which has a greater volume, box D or box E? Explain.
D
7 Add a layer to box D and compare the volumes of
the new box D and box E.
E
270
Lesson 25 Find Volume Using Unit Cubes
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Lesson 25
Name: Find Volume Using Unit Cubes
Solve the problems.
1 What is the volume of this rectangular prism?
How many cubes are
in each layer?
A 12 cubic units
B 13 cubic units
C 30 cubic units
D 60 cubic units
2 What is the volume of this box?
How many layers of
cubes will there be if
you fill the box?
A 6 cubic centimeters
B 10 cubic centimeters
3 cm
C 15 cubic centimeters
D 30 cubic centimeters
5 cm
2 cm
Cindy chose B as the correct answer. How did she get
that answer?
3 Draw or describe a different rectangular prism that has
the same volume as the prism in problem 1.
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What are some
factors of the
number that tells
the volume in
problem 1?
Lesson 25 Find Volume Using Unit Cubes
271
Solve.
4 Which expressions can be used to find the volume of
There is more than
one way to find the
volume of a
rectangular prism.
this rectangular prism? Circle the letter of all that
apply.
A 6 1 4 1 1
B 6 1 6 1 6 1 6 1 6 1 6
C 6 3 1
D 6 1 6 1 1
E6 3 6 3 1
5 If you add 2 layers to the rectangular prism in
What does the
problem ask you to
find?
problem 4, how much greater is the volume?
Show your work.
Solution: 6 Mr. Carlo is building a storage box in his workshop.
The space where he plans to put the box is 5 feet long
and 2 feet wide. He wants the volume of the box to be
at least 36 cubic feet, but no more than 56 cubic feet.
How tall should Mr. Carlo make the box? Explain.
You can start by
finding the number
of cubic feet in
1 layer.
Show your work.
? ft
5 ft
2 ft
Solution: 272
Lesson 25 Find Volume Using Unit Cubes
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